category as a title with posts listed underneath?

https://ivykennedy.com/home2/

hello there. i’m brand new at wordpress. i do a little editing for work, but i know nothing about customizing templates.

how do i get all the posts from a category listed with the category as a title on top of the list?
for example: https://www.ivykennedy.com/trash/Screen%20shot%202013-06-08%20at%204.58.53%20PM.png
Concerts being the category/title, ticket stubs, pearl jam, met gavin rossdale as posts.

also how is this done in two columns on the front/home page?

P.S. I’d like to keep the Ivy Vine banner across the top and maybe have a picture slideshow somewhere on the front/home page.

thank you so much for your help.